Methods for estimating a distance, normally used for measuring distances in one dimension only, are already known. Some systems were based on ultrasonic methods, which detect the echo of the pulse and utilise highly directional transducers pointing towards the target, in order to measure the position and distance. With such technique, the distance between a transducer and a receiver is indirectly determined by means of the elapsed time, normally called “flight time”, during which the signal generated at the transmitter impinges on the receiver and is reflected back to the transmitter.
Distances are determined by measuring the elapsed time starting from the emission of the pulse that travels from the transmitter to each of the receivers. The computation of coordinates is usually done using simple triangulation and/or lateration.
More recently, sensors and distributed calculus systems in combination with high-density wireless networks for the collection and the distribution of environmental data, have become widespread, due to their important relation with problems like public welfare, society, environment protection, etc. The basic idea consists in distributing in a space region a great number of sensors with all-sufficient supply and having a low unitary cost, capable of forming the nodes (branch points) of a wireless network, of acquiring data, and of performing simple processing operations. These sensors may for instance include temperature sensors, humidity sensors, illumination sensors, acoustic microphones or ultrasonic sensors, magnetic sensors, inertial sensors, or optical sensors.
A typical goal of a sensor network is to detect, monitor and classify objects or events, or to measure the value of parameters in the neighborhood of this network.
For example, one can imagine to construct the network nodes as small as maize seeds, provided with micro-batteries and capable of measuring the temperature and humidity, of transmitting the acquired data to a radio base, and above all, of determining their own position (localization) with respect to a given reference frame. A farmer could “seed” the nodes of the network in a maize field, and these would then transmit an accurate map of the temperature and humidity of the soil detected on the whole field. Other very promising applications concern home automation (domotics) and will allow to monitor the position and parameters of objects and persons inside a house, to govern the management of storehouses, and more generally the logistics, in order to be able to determine the position and to control the flow of products, and lastly, to perform the automatic survey of excavations and manufactured articles.
In general, the network structure can be “summed up” as follows: a certain number of low-cost nodes provided with adequate sensor properties, with limited processing capabilities, and provided with a communication system with a low energy consumption, are distributed inside a given space region. The measured entities are pre-processed locally, and the result is transmitted to a local central station (Central Information Processor, CIP) through a low-power communication network. The CIP system processes the information transmitted from the sensors and sends the result to a processing centre of higher hierarchical level [1, 2, 3, 4, 5, 6]. Certain algorithms for processing the data provided by the sensors present in the network nodes assume that the position of each node is given [7]. However, often a sufficiently accurate knowledge of the node positions is not available. The single nodes are often positioned on the field by persons, or by throwing them from aeroplane platforms. A particular case concerns nodes provided with position sensors. These nodes may for instance be positioned on objects or persons whose position it is desired to continuously monitor in time, and the desired output from the system then consists in the knowledge of the position of each sensor with respect to a reference frame.
To this end, each node could be provided with a Global Positioning System (GPS), but this solution would be very expensive and would increase significantly the energy consumption of each node. Moreover, the spatial resolution provided by the GPS could be insufficient for many applications, like the accurate determination of the position (localization) of objects and persons inside a house. Self-localization in networks of sensors is nowadays a very active field of research [3, 7, 8, 9].